Cherenkov radio pulses from electromagnetic showers in the time-domain

The electric field of the Cherenkov radio pulse produced by a single charged particle track in a dielectric medium is derived from first principles. An algorithm is developed to obtain the pulse in the time domain for numerical calculations. The algorithm is implemented in a Monte Carlo simulation of electromagnetic showers in dense media (specifically designed for coherent radio emission applications) as might be induced by interactions of ultra-high energy neutrinos. The coherent Cherenkov radio emission produced by such showers is obtained simultaneously both in the time and frequency domains. A consistency check performed by Fourier-transforming the pulse in time and comparing it to the frequency spectrum obtained directly in the simulations yields, as expected, fully consistent results. The reversal of the time structure inside the Cherenkov cone and the signs of the corresponding pulses are addressed in detail. The results, besides testing algorithms used for reference calculations in the frequency domain, shed new light into the properties of the radio pulse in the time domain. The shape of the pulse in the time domain is directly related to the depth development of the excess charge in the shower and its width to the observation angle with respect to the Cherenkov direction. This information can be of great practical importance for interpreting actual data.